It is well known that a Generalized Decision Feedback Equalizer (GDFE) based precoder provides the optimal capacity solution for Multi-user Multiple-Input Multiple-Output (MU-MIMO) wireless systems. However, the computational cost of determining various filters associated with the GDFE Precoder is often prohibitive and is not suitable for many practical systems.
There are several known Precoding techniques which can enable a Base Station (BS) equipped with multiple antennas to send simultaneous data streams to multiple user terminals (UTs) in order to optimize system capacity. In general, Precoding for a MU-MIMO system aims to optimize a certain criterion such as system capacity or bit error rate. Selected references are noted below, together with a description of relevant aspects of the techniques proposed therein.
Q. H Spencer, A. L. Swindlehurst, and M. Haardt, “Zero-forcing methods for downlink spatial multiplexing in multi-user MIMO channels”, IEEE Transactions on Signal Processing, pp. 461-471, February 2004 [1] describes a linear precoding technique, known as Block Diagonalization (BD), which separates out the data streams to different UTs by ensuring that interference spans the Null Space of the victim UT's channel. The BD technique diagonalizes the effective channel matrix so as to create multiple isolated MIMO sub-channels between the BS and the UTs. Although this scheme is simple to implement, it limits system capacity somewhat.
C. Windpassinger, R. F. H Fischer, T. Vencel, and J. B Huber, “Precoding in multi-antenna and multi-user communications”, IEEE Transactions on Wireless Communications, pp. 1305-1316, July 2004 [2] describes a non-linear precoding scheme known as Tomlinson-Harashima Precoding (THP). This scheme relies on successive interference pre-cancellation at the BS. A modulo operation is used to ensure that transmit power is not exceeded. Different from BD, THP triangularizes the effective channel matrix and provides somewhat higher system capacity when compared to BD.
In W. Yu, “Competition and Cooperation in Multi-User Communication Environments”, PhD Dissertation, Stanford University, February 2002 [3] and W. Yu and J. Cioffi, “Sum capacity of Gaussian vector broadcast channels”, IEEE Transactions on Information Theory, pp. 1875-1892, September 2004 [4], Wei Yu introduced the GDFE Precoder and showed that it achieves a high degree of system capacity. The basic components of this scheme are illustrated in FIG. 1. The GDFE Precoder includes an interference pre-cancellation block 101. Similar to the THP precoding scheme discussed in reference [2] above, the interference pre-cancellation helps to ensure that the symbol vector encoded at the kth step will suffer from the interference from (k-1) symbol vectors only. Information symbols u are processed by the interference pre-cancellation block 101 to produce filtered vector symbols x.
The filtered vector symbols x are then passed through a transmit filter 103 denoted by matrix B to produce transmitted signals y. In reference [3] and [4], a technique based on the covariance matrix (Szz) corresponding to “Least Favorable Noise” is proposed to compute the GDFE Precoder components. Although, this technique achieves a high degree of system capacity, the computational cost of determining the GDFE Precoder components is effectively prohibitive for a real-time implementation required by most practical systems.
X. Shao, J. Yuan and P. Rapajic, “Precoder design for MIMO broadcast channels”, IEEE International Conference on Communications (ICC), pp. 788-794, May 2005 [5] proposes a different precoding technique which achieves a capacity close to the theoretical maximum system capacity. The proposed method is computationally less complex compared to the GDFE Precoder technique. However, the proposed method allocates equal power to all data streams, which may not be an effective technique for practical systems using a finite number of quantized bit-rates. Also, the proposed technique is limited to invertible channel matrices, which may not always be the case.
N. Jindal, W. Rhee, S. Vishwanath, S. A. Jafar, and A. Goldsmith, “Sum Power Iterative Water-filling for Multi-Antenna Gaussian Broadcast Channels”, IEEE Transactions on Information Theory, pp. 1570-1580, April 2005 [6] derives a very useful result referred to as the MAC/BC (multiple access channel/broadcast channel) duality.; and Wei Yu, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 66, “Advances in Network Information Theory,” pp. 159-147 [7] develops the concept of least favorable noise.